An experiment has been carried out to verify the existence of the resonant interaction between trains of gravity waves, predicted by Phillips (1960). As suggested by Longuet-Higgins (1962), two trains of waves in mutually perpendicular directions were generated in a rectangular wave tank. The ratio σ1/σ2 of the wave frequencies was varied (1·4 < σ1/σ2 < 2·1). When σ1/σ2 [eDot ] 1·7357 it was expected that a resonant interaction would take place, generating a wave of frequency (2σ1−σ2). The amplitude of the third wave was expected to increase almost linearly in the direction of wave propagation. The shape of the response curve as a function of σ1/σ2 was also predicted.

In the present experiments rather large wave amplitudes had to be used, and the theoretical shape of the response curve was distorted by non-linear detuning. Nevertheless the peak amplitude of the resonant wave was found to increase with distance in very nearly the manner predicted.

These experiments were carried out in 1961 but publication was deferred pending a similar but more accurate investigation by McGoldrick, Phillips, Huang & Hodgson (1966). Much of the theoretical discussion given in the present paper is relevant to their work.

This paper presents the results of experiments on the resonant interaction of gravity waves. Two mutually-orthogonal primary wave trains are generated in a tank and their interaction products studied at various positions on the surface. Under suitable conditions, the growing resonant third-order interaction product is identified; its amplitude is shown to be a linear function of the interaction distance. The band-width of the response decreases with increasing distance, as is characteristic of the phenomenon of resonance. The ratio of the frequencies of the primary waves at resonance is very close to that predicted theoretically; the growth rate of the third component is close to, though about 20% higher than, the predicted value. Conditions far from resonance are also studied; it is found that the growing tertiary wave is absent in this case.

These results offer the first unambiguous experimental demonstration of resonant wave interactions.

When a semi-infinite flat plate is immersed parallel to an unbounded, plane, steady, asymmetric, constant shear flow of an incompressible viscous fluid, an interaction occurs between the surface-generated vorticity and the external vorticity. A physical assumption was made in a previous paper (Mark 1962) concerning this problem that the pressure field in a thin layer adjacent to the top-side of the plate may be accurately approximated by the undisturbed constant-pressure field—that which exists before the insertion of the plate into the flow. This means that the vorticity interaction is assumed to have no effect on the undisturbed pressure field. That this is a valid first approximation far downstream along the plate where the interaction is intense is given rigorous support in this paper.

The flow below the plate is examined on a heuristic basis. It is found that there is a strong possibility for the flow to separate from the lower surface near the leading edge of the plate. However, far downstream the flow settles down to a Stokes-type flow near the plate.

A second approximation for the velocity of a large gas bubble in an infinite liquid is derived from a linear perturbation of the first approximation. Previously known experimental results are in excellent agreement with the resulting velocity, \[ U = 0.652(g\overline{a})^{\frac{1}{2}}, \] where $\overline{a}$ is the apparent radius of curvature of the front part of the bubble, and g the acceleration due to gravity. The shape of this second approximation is seen to be indistinguishable from spherical over a large region near the front stagnation point.

The paper presents the results of measurements of fluctuating lift and drag on a long square cylinder. The measurements include the correlation of lift along the cylinder and the distribution of fluctuating pressure on a cross-section. The magnitude of the fluctuating lift was found to be considerably greater than that for a circular cross-section and the spanwise correlation much stronger.

It was found that the presence of large-scale turbulence in the stream had a marked influence on both the steady and the fluctuating forces. The most significant changes were at small angles of attack (%alpha; < 10°) and included a reduction in base suction and a decrease in fluctuating lift of about 50%.

The present experiments lay a foundation for a detailed study of interface propagation in a mixed laminar–turbulent flow between counter-rotating concentric cylinders. Such mixed flows, including one particularly well-organized pattern called spiral turbulence, are found to be a dominant feature of transition in Couette flow. In spiral turbulence, the laminar and turbulent regions of the flow form an alternating pattern of helical stripes, rotating with approximately the mean angular velocity of the two cylinders. Stable right-handed or left-handed spirals occur with equal probability when the flow is established from rest. Hot-wire measurements have been made of the mean cross-sectional shape of the interfaces in the axial mid-plane for a spiral-turbulent flow having low dispersion in the interface position. A nose of turbulence associated with the leading interface projects into the laminar region near the outer cylinder, while a corresponding tail is associated with the trailing interface near the inner cylinder. Fluctuations in interface position and in apparent length of the turbulent region are closely Gaussian, and the fluctuations are rapid compared with the period of rotation of either cylinder.

Measurements at moderately large Reynolds numbers in a finite laminar circular Couette flow show that the tangential motion near the axial plane of symmetry is two-dimensional, within experimental accuracy, but is nevertheless strongly modified by end conditions.

The study of free oscillations of a homogeneous liquid under gravity in rotating rectangular basins of uniform depth is undertaken from both theoretical and experimental considerations.

The theoretical study is in the framework of the quasistatic equations. It is also assumed that the curvature of the free surface can be ignored. Numerical computations for the frequencies and modal structures were carried out for several of the slowest antisymmetric and symmetric modes in a square basin and in a rectangular basin of two-to-one dimension ratio, without any restriction on the angular speed of rotation of the basin. These computations are in agreement with a numerical value obtained many years ago by Taylor, and also with several values found by Corkan & Doodson. They exhibit the typical frequency-splitting associated with certain multiplets in the zero-rotation spectrum. Further, the theoretical calculations indicate that the slopes of the curves of frequency versus speed of rotation change sign for some of the modes in rectangular geometry. Such behaviour is not present in circular basins. Negative modes are found to be ‘unstable’ in the sense of Corkan & Doodson; that is, they are transformed into positive modes for sufficiently high rotation. Calculations were also made for the slowest longitudinal oscillations in highly elongated basins to demonstrate the decreasing importance of rotation on the frequencies of these modes.

Experimental work was carried out in a flat-bottomed square tank for the slowest positively and negatively propagating antisymmetric modes and the slowest positively propagating symmetric mode. Good agreement was found between theory and experiment.

A theory is developed for an incompressible fluid in a steady three-dimensional rotational flow. Solutions are obtained subject to the restriction of small perturbations and are determinant provided that the vorticity distribution along the axis of rotation is known. Effects of viscosity are included. Closed-form expressions for the zeroth-order circulation and stream function and first-order circulation are given, with other higher-order expressions requiring high-speed computers. Experimental results of radial variation of axial velocity in the core show a distribution more elaborate than Gaussian.

The problem considered is the entry of a thin symmetric wedge impinging normally on the free surface of a compressible inviscid liquid, gravitational effects being neglected. Since the body is thin, the problem is a linear one, and its solution is possible for the whole range of Mach numbers of the body's motion in the liquid. It is shown that the free-surface elevations are lowered considerably as the Mach number increases, and that the presence of the free surface acts so as to lower the pressure differences arising from compressibility.

An approximate expression is obtained for the force on an arbitrary body executing slow vibrations in a viscous fluid.

The equation which was proposed for the calculation of forces on a sphere accelerating in a viscous fluid is verified by comparing the velocities of spheres falling under gravity in a viscous fluid with those calculated from the equation.

Existing data on the condensation of steam and moist air in supersonic nozzles are compared with predictions based on nucleation and drop-growth theory. It is concluded that, if the surface tension is assumed independent of curvature, and the classical liquid-drop theory (based on a stationary liquid drop) is used, the theory is in general agreement with the data. The effects of uncertainties in cluster surface energy and also of the large corrections to nucleation theory due to the ‘gasification’ concept are examined. The gasification correction is in accord with experimental data only if the surface tension is considered to rise significantly with curvature. In neither case can the Tolman or Kirkwood–Buff equations be supported. A review of existing data shows that there is some question as to the appropriate value of the condensation coefficient but this is of little consequence as long as the accommodation coefficient for the liquid–vapour surface is taken to be unity. The usefulness of the nozzle experiments for testing the validity of nucleation theory is demonstrated.

The present paper studies the interaction between non-equilibrium ionization phenomena in a plasma and the non-uniform flow of that plasma. The characteristics of non-equilibrium conditions are reviewed for the uniform flow situation in which electric and magnetic fields may exist. In order to permit study of the non-uniform flow situation a single-fluid theory is proposed in which the electrical conductivity is assumed to be a function of the absolute magnitude of the current density. The resulting highly simplified system of equations are then used to formulate the Hartmann-flow problem. For this case the formerly linear problem becomes non-linear. Despite this, solutions to within a quadrature are obtained when the Hall effect is neglected. The more complex problem including the Hall effect is solved numerically. Solutions showing velocity and current profiles are given. For certain values of the parameters governing the problem it is shown that no solutions exist.